The noncommutative geometry dictated by physics is then given by the product of the ordinary 4-dimensional continuum by a finite noncommutative geometry \(({\mathcal {A}}_F,{\mathcal {H}}_F,D_F)\)  which appears naturally from the classification of finite geometries of \(KO\) -dimension equal to 6 modulo 8 (cf.[1]}, [2]}). The finite dimensional algebra \({\mathcal {A}}_F\)  which appeared is of the form
\({\mathcal {A}}_F=C_{+}\oplus C_{-}; \qquad C_{+}=M_{2}(\mathbb {H}),\ \ \ C_{-}=M_{4}(\mathbb {C}).\) 
